A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board? - Mathematics

Advertisements
Advertisements

A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

Advertisements

Solution

Side of traffic signal board = a

Perimeter of traffic signal board = 3 × a

`2s = 3a rArr s = 3/2 a`

By heron's formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of given triangle "= sqrt(3/2 a(3/2a-a)(3/2a-a)(3/2a-a))`

                                   `= sqrt((3/2a)(a/2)(a/2)(a/2))`

                                   `= sqrt3/4a^2"                   ..........(1)"`

Perimeter of traffic signal board = 180 cm

Side of traffic signal board (a)=(180/3)cm = 60 cm

Using equation (1), area of traffic signal board

`= sqrt3/4(60cm)^2`

`= (3600/4sqrt3)cm^2 = 900sqrt3 cm^2`

 

  Is there an error in this question or solution?
Chapter 12: Heron's Formula - Exercise 12.1 [Page 202]

APPEARS IN

NCERT Mathematics Class 9
Chapter 12 Heron's Formula
Exercise 12.1 | Q 1 | Page 202

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Sides of a triangle are in the ratio of 12: 17: 25 and its perimeter is 540 cm. Find its area.


An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.


Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.


Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.

 

Find the area of an isosceles triangle having the base x cm and one side y cm.

 

Sides of a triangle are cm 45 cm, 39 cm and 42 cm, find its area.


Look at the measures shown in the adjacent figure and find the area of ☐ PQRS.


Some measures are given in the adjacent figure, find the area of ☐ABCD.


Find the areas of given plot. (All measures are in metres.)


Find the areas of the given plot. (All measures are in metres.)


Find the area of the triangle formed by the points

(1, – 1), (– 4, 6) and (– 3, – 5)


Find the area of the triangle formed by the points

(–10, –4), (–8, –1) and (–3, –5)


Determine whether the sets of points are collinear?

(a, b + c), (b, c + a) and (c, a + b)


If the points A(– 3, 9), B(a, b) and C(4, – 5) are collinear and if a + b = 1, then find a and b


A triangular shaped glass with vertices at A(– 5, – 4), B(1, 6) and C(7, – 4) has to be painted. If one bucket of paint covers 6 square feet, how many buckets of paint will be required to paint the whole glass, if only one coat of paint is applied


Find the area of triangle AGF


Find the area of triangle FED


The area of triangle formed by the points (− 5, 0), (0, – 5) and (5, 0) is


A man walks near a wall, such that the distance between him and the wall is 10 units. Consider the wall to be the Y-axis. The path travelled by the man is


The area of a triangle is 5 sq. units. Two of its vertices are (2, 1) and (3, −2). The third vertex is (x, y) where y = x + 3. Find the coordinates of the third vertex.


Find the area of a triangle formed by the lines 3x + y – 2 = 0, 5x + 2y – 3 = 0 and 2x – y – 3 = 0


Using Heron’s formula, find the area of a triangle whose sides are 10 cm, 24 cm, 26 cm


Using Heron’s formula, find the area of a triangle whose sides are 1.8 m, 8 m, 8.2 m


The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of ₹ 20 per m2 


The perimeter of a triangular plot is 600 m. If the sides are in the ratio 5 : 12 : 13, then find the area of the plot


Find the area of an equilateral triangle whose perimeter is 180 cm


An advertisement board is in the form of an isosceles triangle with perimeter 36 m and each of the equal sides are 13 m. Find the cost of painting it at ₹ 17.50 per square metre.


Find the area of the unshaded region


The semi-perimeter of a triangle having sides 15 cm, 20 cm and 25 cm is 


The perimeter of an equilateral triangle is 30 cm. The area is


The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?


A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.


A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2 . Find the cost of painting.


The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.


A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1 m2 of the field, find the total cost of ploughing the field.


Share
Notifications



      Forgot password?
Use app×